52 research outputs found
A PDE-like Toy-Model of Territory Working
This note introduces a PDE-like Toy-Model that embeds several aspects of
Territory Working. The long term goal is to build a software tool that behaves
like a Territory, and in particular that incorporates its
multi-scale-in-time-and-space nature, in order to make simulations, to explore
scenarios, to foresee policy impacts, to help to make a decision when facing a
change in the environment or in cultural behavior, {\it etc.}. The aim of this
note is prove that the concept of building a model that couple Systemic
Approach and PDE tools to achieve the evoked long term goal is possible
Models for cohesive sediments describing the evolution of the characteristics of particles
The goal of this paper is to set up a framework designed to take into account
the characteristics of sediment particles when transported by water. Our
protocol consists in describing the characteristics of sediment particles via
an additional variable, and to build operators involving this new variable,
modeling the evolution of the particle characteristics. Several such operators
are proposed, some based on principles of relaxation toward an equilibrium, and
others on a description of the particles' aggregation and fragmentation
process. A discrete version of the latter is also offered for numerical
settings
Application of the averaging method to the gyrokinetic plasma
we show that the solution to an oscillatory-singularly perturbed ordinary
differential equation may be asymptotically expanded into a sum of oscillating
terms. Each of those terms writes as an oscillating operator acting on the
solution to a non oscillating ordinary differential equation with an
oscillating correction added to it. The expression of the non oscillating
ordinary differential equations are defined by a recurrence relation. We then
apply this result to problems where charged particles are submitted to large
magnetic field
Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates
In this paper, we present some new results about the approximation of the
Vlasov-Poisson system with a strong external magnetic field by the 2D finite
Larmor radius model. The proofs within the present work are built by using
two-scale convergence tools, and can be viewed as a new slant on previous works
of Fr\'enod and Sonnendr\"ucker and Bostan on the 2D finite Larmor Radius
model. In a first part, we recall the physical and mathematical contexts. We
also recall two main results from previous papers of Fr\'enod and
Sonnendr\"ucker and Bostan. Then, we introduce a set of variables which are
so-called canonical gyrokinetic coordinates, and we write the Vlasov equation
in these new variables. Then, we establish some two-scale convergence and
weak-* convergence results
An Attempt at Classifying Homogenization-Based Numerical Methods
International audienceIn this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes
A PDE-like Toy-Model of Territory Working
International audienceThis note introduces a PDE-like Toy-Model that embeds several aspects of Territory Working. The long term goal is to build a software tool that behaves like a Territory, and in particular that incorporates its multi-scale-in-time-and-space nature, in order to make simulations, to explore scenarios, to foresee policy impacts, to help to make a decision when facing a change in the environment or in cultural behavior, {\it etc.}. The aim of this note is prove that the concept of building a model that couple Systemic Approach and PDE tools to achieve the evoked long term goal is possible
Un exemple d'application des mathématiques à l'environnement littoral : La dynamique à long terme des dunes marines dans les zones soumises à la marée. Modélisation, Analyse, Homogénéisation et Simulation
International audienceUn modèle de dynamique à long terme des dunes marines dans les zones soumises à la marée est construit et analysé. Une méthode numérique basée sur de l'homogénéisation est proposée pour le simuler
- …